Chung and Hulbert [1]} introduced the generalized-\(\alpha \)  method for hyperbolic systems arising in structural dynamics; later, Hulbert and Chung [2]} presented an explicit version of this time-marching method. The method is second-order accurate in time and provides user-control on the high-frequency numerical dissipations. Likewise, other well-known methods like, e.g., the Newmark-\(\beta \)  [3]} and the HHT-\(\alpha \)  [4]} methods have both implicit and explicit formulations and are limited to the second-order accuracy. Nevertheless, the Newmark method does not control the dissipation while, using the HHT-\(\alpha \) , one obtains dissipative solutions in low-frequency regions. The generalized-\(\alpha \)  method produces an algorithm that combines high-frequency and low-frequency dissipations optimally; see [1]}, [2]}.
